Brain white matter connections have become a focus of major interest with important maturational processes occurring in newborns. To study the complex microstructural developmental changes in-vivo, it is imperative that non-invasive neuroimaging approaches are developed for this age-group. Multi-b-value diffusion weighted imaging data were acquired in 13 newborns, and the biophysical compartment diffusion models CHARMED-light and NODDI, providing new microstructural parameters such as intra-neurite volume fraction (νin) and neurite orientation dispersion index (ODI), were developed for newborn data. Comparative analysis was performed and twenty ROIs in the white matter were investigated. Diffusion tensor imaging and both biophysical compartment models highlighted the compact and oriented structure of the corpus-callosum with the highest FA and νin values and the smallest ODI values. We could clearly differentiate, using the FA, νin and ODI, the posterior and anterior internal capsule representing similar cellular structure but with different maturation (i.e. partially myelinated and absence of myelin, respectively). Late maturing regions (external capsule and periventricular crossroads of pathways) had lower νin values, but displayed significant differences in ODI. The compartmented models CHARMED-light and NODDI bring new indices corroborating the cellular architectures, with the lowest νin, reflecting the late maturation of areas with thin non-myelinated fibers, and with highest ODI indicating the presence of fiber crossings and fanning. The application of biophysical compartment diffusion models adds new insights to the brain white matter development in vivo.